Please help me with this question

x = 8

Step-by-step explanation:

Since < A and < B are vertical angles, then it means that they have the same measure.

Given that m < A = (3x - 21)°, and m < B = (2x - 13)°:

We can set up the following equation to solve for the value of x:

m < A  = m < B

(3x - 21)° = (2x - 13)°

3x - 21 = 2x - 13

Subtract 2x from both sides:

3x - 2x - 21 = 2x - 2x - 13

x - 21 = -13

Add 21 to both sides to isolate and solve for the value of x:

x - 21 + 21 = -13 + 21

x = 8

We must verify if we have the correct value for x by plugging in 8 into the equality statement:

(3x - 21)° = (2x - 13)°

[3(8) - 21]° = [2(8) - 13]°

(24 - 21)° = (16 - 13)°

3° = 3° (True statement. This means that we have the correct value for x).

Therefore, the value of x = 8.

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answer is 8x+24

area of vanessa's patio = length × width

given, length = (3x² + 5x + 10)

width = (x² - 3x - 1)

area of vanessa's patio = (3x² + 5x + 10)(x² - 3x - 1)

= 3x²(x² - 3x - 1) + 5x(x² - 3x - 1) + 10(x² - 3x - 1)

= 3x⁴ - 9x³ - 3x² + 5x³ - 15x² - 5x + 10x² - 30x - 10

= 3x⁴ - 4x³ - 8x² - 35x - 10

hence, expression of vanessa's patio = (3x⁴ - 4x³ - 8x² - 35x - 10)